Question

write the negative of the following 3 is not a root of the equation x 2 +3x - 18 =0,​

Answer 1

Answer:

First, please formulate your question properly. You have asked: “What is x2–3x−18=0 ?” And my honest answer would be “A quadratic equation!” I bet that this was not your question. I assume that you wanted to know “What is x if x2–3x−18=0?

And the answer to this question is: You can either proceed with completion of the square or by using the well known formula for solving quadratic equation. Completion of the square is more educational, so I will proceed with this one.

You start moving the absolute term -18 to the right hand side:

x2–3x=18

Then complete the left hand side to fit the binomial formula by adding a new constant, and make sure that constant is added on the right as well:

x2–3x+9/4=18+9/4

Next apply the binomial formula on the left, and add the two summands on the right. What you get on the right hand side is called the discriminant of the equation.

(x−3/2)2=81/4

Extracting roots on both sides (mind the sign) gives you two options

x−3/2=9/2 and x−3/2=−9/2

From where you get the two possible values for x:

x=12/2=6 , and x=−6/2=−3.